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2015 Polynomiography Based on the Nonstandard Newton-Like Root Finding Methods
Krzysztof Gdawiec, Wiesław Kotarski, Agnieszka Lisowska
Abstr. Appl. Anal. 2015: 1-19 (2015). DOI: 10.1155/2015/797594

Abstract

A survey of some modifications based on the classic Newton’s and the higher order Newton-like root finding methods for complex polynomials is presented. Instead of the standard Picard’s iteration several different iteration processes, described in the literature, which we call nonstandard ones, are used. Kalantari’s visualizations of root finding process are interesting from at least three points of view: scientific, educational, and artistic. By combining different kinds of iterations, different convergence tests, and different colouring we obtain a great variety of polynomiographs. We also check experimentally that using complex parameters instead of real ones in multiparameter iterations do not destabilize the iteration process. Moreover, we obtain nice looking polynomiographs that are interesting from the artistic point of view. Real parts of the parameters alter symmetry, whereas imaginary ones cause asymmetric twisting of polynomiographs.

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Krzysztof Gdawiec. Wiesław Kotarski. Agnieszka Lisowska. "Polynomiography Based on the Nonstandard Newton-Like Root Finding Methods." Abstr. Appl. Anal. 2015 1 - 19, 2015. https://doi.org/10.1155/2015/797594

Information

Published: 2015
First available in Project Euclid: 15 April 2015

zbMATH: 06619916
MathSciNet: MR3319148
Digital Object Identifier: 10.1155/2015/797594

Rights: Copyright © 2015 Hindawi

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